Sensors having signal redundancy

ABSTRACT

Methods and apparatus for combining redundant signals to generate outputs signals with enhanced accuracy and/or risk level. In embodiments, first signals are generated by a first transducer and second signals are generated by a second transducer. In other embodiments, first signals are generated by a first die and second signals are generated by a second die. An amount of overlap between error distributions of the first and second signals can be used to detect failure and/or indicate risk of failure.

BACKGROUND

The trend towards advanced driver-assistance systems (ADA) andautonomous vehicles is leading to more stringent requirements on sensorICs and systems. Four automotive safety integrity levels (ASIL A, B, Cand D) are defined by the ISO 26262 functional safety for road vehiclesstandard. ASIL D dictates the highest integrity requirements. At thesensor level, an ASIL D rating can be achieved through homogeneousredundancy (i.e., two sensor ICs using the same technology, such as Hallelements or magnetoresistive elements, in a single package) orheterogeneous redundancy, e.g., two sensor ICs using different sensingtechnologies, or one sensor IC including two sensing technologies, forexample Hall elements or magnetoresistive elements. Some safety criticalapplications may require the use of more than two sensor ICs to enablevoting.

SUMMARY

Embodiments of the invention provide methods and apparatus for combiningredundant signals from the channels of multiple devices for improvedsafety level and accuracy. While example embodiments are shown anddescribed in conjunction with dual channel angle sensors includingSIN/COS angle sensors, it is understood that embodiments of theinvention are applicable to sensors in general in which improved safetylevel and accuracy are desirable.

In one aspect, a method comprises: receiving first signals from a firstsignal source; receiving second signals from a second signal source,wherein the first and second signals are redundant; and combining thefirst signals and the second signals to generate a first output signalfrom the first signals, a second output signal from the second signals,and a third output signal from the first signals and the second signals.

A method can further include one or more of the following features:generating a fourth output signal from first and second signalsproviding risk information, the first signal source comprises a firsttransducer and the second signal source comprises a second transducer,the first and second transducers are substantially similar, the firstsignal source comprises a first die and the second signal sourcecomprises a second die, the third output signal comprises an average (orweighted average, or any combination) of the first and second signals,the third output signal is more accurate than the first or second outputsignals, the first and second signals each comprise sine and cosinevalues, the first, second, and third output signals each comprise anangle output signal, generating a fourth output signal from first andsecond signals providing risk information based on a comparison ofsimilarity of the first signals and the second signals, the comparisonof similarity includes using a threshold based on degrees for anglesignals generated from sine and cosine signals, assigning a first errordistribution to the first signals and a second error distribution to thesecond signals, assigning rectangular functions to the first and seconderror distributions, assigning a given number of standard deviations todefines the rectangular functions, determining an amount of overlapbetween the first and second error distributions, determining a failurecondition based on the amount of overlap, determining a level ofconfidence in the first and/or second signals from the amount ofoverlap, and/or determining a best estimate for the first and/or secondsignals from the amount of overlap.

In another aspect, a system comprises: a first signal source configuredto generate first signals; a second signal source to generate secondsignals, wherein the first and second signals are redundant; and asignal processing module configure to combine the first signals and thesecond signals to generate a first output signal from the first signals,a second output signal from the second signals, and a third outputsignal from the first signals and the second signals.

A system can further include one or more of the following features: thesignal processing module is further configured to generate a fourthoutput signal from first and second signals providing risk information,the first signal source comprises a first transducer and the secondsignal source comprises a second transducer, the first and secondtransducers are substantially similar, the first signal source comprisesa first die and the second signal source comprises a second die, thethird output signal comprises an average of the first and secondsignals, the third output signal is more accurate than the first orsecond output signals, the first and second signals each comprise sineand cosine values, the first, second, and third output signals eachcomprise an angle output signal, generating a fourth output signal fromfirst and second signals providing risk information based on acomparison of similarity of the first signals and the second signals,the comparison of similarity includes using a threshold based on degreesfor angle signals generated from sine and cosine signals, assigning afirst error distribution to the first signals and a second errordistribution to the second signals, assigning rectangular functions tothe first and second error distributions, assigning a given number ofstandard deviations to defines the rectangular functions, determining anamount of overlap between the first and second error distributions,determining a failure condition based on the amount of overlap,determining a level of confidence in the first and/or second signalsfrom the amount of overlap, and/or determining a best estimate for thefirst and/or second signals from the amount of overlap.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing features of the invention, as well as the invention itselfmay be more fully understood from the following detailed description ofthe drawings, in which:

FIG. 1 is a high level block diagram of an example sensor system havingmultiple transducers generating an approximation of sensed data,redundant and risk assessment signals;

FIG. 2 is a schematic representation of an example sensor system havingmultiple transducers generating an approximation of sensed data,redundant and risk assessment signals;

FIG. 2A is a schematic representation of an example sensor system havingmultiple die generating redundant and risk assessment signals;

FIG. 3A is a graphical representation of a data point from anon-redundant sensor on a trigonometric circle;

FIG. 3B is a graphical representation of the data point of FIG. 3A withan error distribution;

FIG. 4A is a graphical representation of redundant first and second datapoints and respective error distributions;

FIG. 4B is a graphical representation of the first and second datapoints of FIG. 4A with example rectangular-approximated errordistributions;

FIG. 5 is a representation of intersection over union with overlappingand combined regions for risk assessment with redundant data points;

FIG. 6 is a flow diagram for generating and processing redundant datapoints; and

FIG. 7 is a schematic representation of an example computer than canperform at least a portion of the processing described herein.

DETAILED DESCRIPTION

FIG. 1 shows an example system 100 having a first transducer 102 and asecond transducer 104 coupled to a signal processing module 106. Thesignal processing module 106 can receive signals from the first andsecond transducers 102, 104 and generate various output signals(deterministic or probabilistic, e.g. likelihood of observed sampleswhich also be called evidence) with or without combining the signalsfrom the first and second transducers. As described more fully below,the first and second transducers 102, 104 can be the same type oftransducer or different types of transducers.

In the illustrated embodiment, the signal processing module 106generates a T1OUT signal that corresponds to data from the firsttransducer 102 and a T2OUT signal that corresponds to data from thesecond transducer 104. A T*OUT signal, which may be a ‘better’ estimateof the sensed quantity than T1OUT and T2OUT, is generated from acombination of data from the first and second transducers 102, 104. Inembodiments, the signal processing module 106 generates a risk signalthat includes an indication of risk of error based on data from thesignals of the first and/or second transducer 102, 104.

FIG. 2 shows an example system 200 having a first transducer T1 thatgenerates first and second output signals 202, 204. In embodiments, thefirst output signal 202 corresponds to a sine signal for an angle sensorand the second output signal 204 corresponds to a cosine signal for anangle sensor. A first processing block 206 receives the sine signal 202and performs signal conditioning and/or normalization. For example, thesignal is conditioned to remove noise and normalized to be within agiven range. The first processing block 206 provides an output signal toa first combiner block 208 and a second combiner block 210.

A second processing block 212 receives the cosine signal 204 andperforms signal conditioning and/or normalization. The second processingblock 212 provides an output signal to the first combiner block 208 anda third combiner block 222.

In example processing blocks, an arctangent function can be used togenerate an angle from sine and sine signals. In some embodiments,circular vertical Hall elements (CVH) are used to generate sine andcosine signals. In other embodiments, first and second sensors arepositioned in a quadrature relationship to generate sine and cosinesignals. U.S. Pat. No. 7,714,570, which is incorporated herein byreference, describes generating sine and cosine signals and generatingan angle output signal from sine and cosine signals. CORDIC processingand signal look up tables can also be used to generate output angleinformation. One or more features of CVH angle processing may bedescribed in U.S. Pat. Nos. 10,481,220 and 9,007,054, which areincorporated herein by reference.

In the illustrated embodiment, the second transducer T2 generates thirdand fourth output signals 214, 216. In embodiments, the third outputsignal 214 corresponds to a sine signal for an angle sensor and thefourth output signal 216 corresponds to a cosine signal from an anglesensor.

A third processing block 218 receives the sine signal 214 and performssignal conditioning and/or normalization and a fourth processing block220 receives the cosine signal 216 and performs signal conditioningand/or normalization. In the illustrated embodiment, the thirdprocessing block 218 provides an output signal to the third combinerblock 222 and a fourth combiner block 224. The fourth processing block220 provides an output signal to the second combiner block 210 and thefourth combiner block 224.

In the illustrated embodiment, the first combiner block 208 generates anoutput signal 226, which may correspond to an angle output signal basedon the sine and cosine signals 202, 204 from the first transducer. Thefourth processing block 224 generates an output signal 228, which maycorrespond to an angle output signal based on the sine and cosinesignals 214, 216 from the second transducer. The output signals 226, 228can also be provided to a mixing block 230. The mixing block 230 mayreceive output signals from the second and third combiner blocks 210,222. In the illustrated embodiment, the mixing block 230 receives anglesignals generated from each possible sine and cosine combination fromthe first and second transducers.

In embodiments, the mixing block 230 outputs a combined angle signal 232generated from a combination of one or more of the angle signals fromthe combiner blocks 208, 210, 222, 224. In some embodiments, the outputsof the first and fourth combiner blocks 208, 224, are combined, such asaveraged, to generate an angle output signal 232 that may be moreaccurate than the output signals 226, 228, where output signal 226 isgenerated from the first transducer T1 alone and output signal 228 isgenerated from the second transducer T2 alone.

The angle outputs from the combiner blocks 208, 210, 222, 224 can becombined by the mixing block in a variety of ways to meet the needs of aparticular application. In some embodiments, each of angle outputs areaveraged. In other embodiments, some angle outputs are weighted moreheavily than others. For example, the angle outputs from the first andfourth combiner blocks 208, 224 may be weighted more heavily than theangle outputs from the second and third combiner blocks 210, 222. Insome embodiments, angle outputs are combined/processed using Kalmanfiltering which is the statistical best estimate given knowledge ofcurrent signals values and associated error distributions (e.g., maximumlikelihood estimate.

In the illustrated embodiment, the following angles are generated:

Angle calculated from SIN signal of transducer T1 and COS signal oftransducer T1

Angle calculated from SIN signal of transducer T1 and COS signal oftransducer T2

Angle calculated from SIN signal of transducer T2 and COS signal oftransducer T1

Angle calculated from SIN signal of transducer T2 and COS signal oftransducer T2

In the illustrated embodiment, the mixing block 230 outputs a risksignal 234 corresponding to a confidence level in one or more of theangle output signals 226, 232, 228. In embodiments, differences greaterthan a given threshold between two or more of the angle outputs from thecombiner blocks 208, 210, 222, 224 may cause the risk signal 234 totransition to an active state.

In an example embodiment, a difference greater than two degrees betweenthe angle outputs of the output signal 226 generated from the firsttransducer and the output signal 228 generated from the secondtransducer 228 causes the risk signal 234 to transition to an activestate. In another example, a difference greater than five degreesbetween the angle outputs of the angle outputs generated from the secondcombine block 210 and the angle output signal generated by the thirdcombiner block 222 causes the risk signal 234 to transition to an activestate. The difference threshold between compared signals can vary basedon the application, sensor type, user requirement, and the like. Thespecific constraints may constitute part of the hardware safetyrequirements for safety critical applications.

In some embodiments, the risk signal 234 is a digital signal having afirst state that is inactive when risk is less than a selected thresholdand a second state that is active when risk is above the selectedthreshold. In other embodiments, the risk signal 234 provides an analogrisk information as a confidence level, a percentage, values within somerange, or the like.

In example embodiments, risk is considered low or inactive when each ofthe angle output signals 226 (ANG1), 228 (ANG2), 232 (ANG*) aresubstantially the same or within some threshold. As one or more of thesesignals diverge from the other signals, the risk of failure can beconsidered to be active or increased. in another example, Kalman filtersestimate not only the most likely correct value ANG* but also itslikelihood (distribution spread, e.g. standard deviation) which serve asrisk assessment 234.

In one example implementation, a magnetic sensor can sense the angularposition of an engine camshaft that rotates about an axis. Two or moretransducers, die, and/or ICs can be used to sense the position of thecamshaft. The accuracy obtainable from any of the transducers, die,and/or ICs can vary due to axial misalignment of the shaft, inherentmeasurement limitations, temperature changes, process variations and thelike.

FIG. 2A shows a system having some commonality with the system of FIG. 2for first and second die D1, D2 instead of transducers. A firstprocessing block 206′ receives a sine signal from circuitry/sensingelements on a first die D1 and a second processing block 212′ receives acosine signal. The processed signals are provided to first, second,third and fourth combiner blocks 208′, 210′, 222′, 224′, which providesangle output signals to a first mixer block 230′ on the first die.Similarly, processing blocks 250, 252 on the second die provide signalsto combiner blocks 254, 256, 258, 260, which provide angle outputsignals to a second mixer block 262 on the second die. Sine and cosinesignals from the processor blocks 206′, 212′ also provide output signalsto the combiner blocks 254, 256, 258, 260 on the second die and theprocessor blocks 250, 252 on the second die provide output signals tothe combiner blocks 208′, 210′, 222′, 224′ on the first die D1.

The first and second mixer blocks 230′, 262 provide similar angle andrisk signals ANG1, ANG2, ANG*, RISK to a remote system 270, such as anengine control unit (ECU). The ECU 270 can include an equality module272 to compare the signals from the first and second mixer blocks 230′,262. If the angle output signals from the first and second die are notwithin some threshold, a fault signal 274 can become active. In someembodiments, the fault signal 274 may become active if either of therisk signals from mixers 230′, 262 are above a given threshold. Theequality check 272 can be alternatively be integrated in one or repeatedin each sensing system for additional redundancy.

FIG. 3A shows an example representation of a sine, cosine relationship300 shown as a point normalized to lie on a trigonometric circle 302.FIG. 3B shows the effects 304 of electronic noise (thermal noise,flicker noise, dynamic error due to vibrations, etc.) so that the point300 is subject to random disturbances that makes the point fluctuatearound its average position. In embodiments, the point 300 can bemodeled to follow a two-dimensional (2D) gaussian probability densitydistribution represented by 304.

FIG. 4A shows redundant first and second points 400, 402 defined bysine, cosine pairs, each of which is subject to the effects 404, 406 ofnoise and randomness. In an ideal system, the first and secondtransducers/die/etc., provide first and second channels that generatethe same signal. That is, in an ideal system, the redundant first andsecond points 400, 402 are the same point, i.e., they are coincident. Inone implementation example, the first and second points 400, 402 cancorrespond to a sensed magnetic field. In practice, due to sensingelement and electronic mismatch, the positions of the redundant firstand second points 400, 402 are slightly different and may have differentaccuracies, resolutions or noises.

In embodiments, the first and second points 400, 402 are redundant.Redundancy refers to the repetition of two or more signals of same ordifferent nature which entails similar information. One role ofredundancy is to detect one or more failures or anomalies by comparison,or by detection of abnormal combinations of signals.

Redundancy can be global or local to the system. An example of globalsystem redundancy is dual die or stacked die which means that two diesare placed within the same package. Another example of global systemredundancy is the duplication of the hardware, e.g., two or moreintegrated circuits are placed on the PCB. An example of localredundancy is represented by the duplication of a functional blockwithin a system, e.g., two independent temperature sensing systems.

Signal comparison may be performed synchronously (to the best extentdepending on system resources) for a comparison of data of sametemporality. More advanced schemes can be used for value predictionbased on currently available data for a comparison to a future data,e.g. of Kalman filter which uses measurements and predictions from amodel with past data. The latter requires additional temporary datastorage.

As shown in FIG. 4B, in embodiments, the first and second points 400,402, which are redundant, have respective error distributions 408, 410corresponding to the effects 404, 406 shown in FIG. 4A. In exampleembodiments, the error distributions 408, 410 are approximated by a 2Drectangle function centered on the respective sample 400, 402 forgenerating a maximum likelihood estimate. In one embodiment, a Gaussiandistribution is used. It is understood that any suitable distributioncan be used to meet the needs of a particular application.

In embodiments, the error distribution 408, 410 rectangle widths/lengthsare set by noise measures. In one particular embodiment, the values aredetermined using six standard deviations. It is understood that thedistribution 408, 410 widths and lengths can be different but are equalin the illustrated embodiment so as to form squares. The corners of thefirst and second rectangles, here squares, for the distributions 408,410 are defined by the current samples (respectively x,y and x,y) valueand the distribution standard deviation σ:

TABLE 1 Corners Error Distribution 408 Error Distribution 410 Upper Left(x − 3σ, y + 3σ) (x − 3σ, y + 3σ) Upper Right (x + 3σ, y + 3σ) (x + 3σ,y + 3σ) Lower Left (x − 3σ, y − 3σ) (x − 3σ, y − 3σ) Lower Right (x +3σ; y − 3σ) (x + 3σ; y − 3σ)

It is understood that plus and minus 3σ corresponds to six standarddeviations to define the distribution. It if further understood that thenumber of standard variations, as well as the variance in general, canbe selected to meet the needs of a particular application.

FIG. 5 shows an example representation of intersection over union (IoU)for respective error distributions for redundant first and secondpoints. The IoU corresponds to the probability of an event. Theoverlapping region 500 of first and second distributions 502, 504 canform a numerator and a combined region 506 of the first and seconddistributions can form a denominator. The first and second regions 500,502 can correspond to the first and second distributions 408, 410 ofFIG. 4B.

The IoU satisfies the properties of a probability function

Its value is in [0,1]

Its value is maximum when the points agree (complete overlap)

Its value is zero when the points disagree (no overlap)

In embodiments, the IoU value for first and second error distributionscan be used to detect a failure of one or more channels. A center 506 ofthe overlapping region 500 may be a preferred estimate of the sample,such as the samples 400, 402 of FIG. 4A. The IoU value may represent thelevel of confidence (probability) in the measure, as well as a bestpoint estimate for use by the system.

FIG. 6 shows an example sequence of steps for processing redundantsensor signals. In step 600, first sensor signals are received and instep 602, second sensor signals are received. In one embodiment, thefirst sensor signals are generated by a first transducer and the secondsensor signals are generated by a second transducer. In otherembodiments, the first sensor signals are generated on or about a firstdie and the second sensor signals are generated on or about a seconddie.

In step 604, the first and second sensor signals are processed, such asfiltered to remove noise. In step 606, the first and second sensorsignals are combined to generate one or more output signals. In step608, some of the output signals can be mixed. In step 610, redundantdata points of the first and second sensor signals can be assigned errordistributions. In step 612, sensor output signals can be generatedincluding mixed and unmixed signals and risk signals.

In example embodiments, sensor output signals can include a first anglesignal from a first transducer or die, a second angle signal from asecond transducer or die, and a third angle signal of enhanced accuracygenerated from signals from two or more transducers or die. In someembodiments, a risk signal can be generated from redundant data pointsfrom the first and second transducers or die based on respective errordistributions. In embodiments, an amount of overlap of errordistributions for redundant points can be used to quantify risk.

In other embodiments, other suitable techniques to compare errordistributions of redundant points can be used to meet the needs of aparticular application. For example, Bayesian inference or Markovdecision processes approach that estimate the probability of successiveevents and can identify abnormal sequences as proof of a faultybehavior.

As used herein, the term “magnetic field sensing element” is used todescribe a variety of electronic elements that can sense a magneticfield. The magnetic field sensing element can be, but is not limited to,a Hall effect element, a magnetoresistance element, or amagnetotransistor. As is known, there are different types of Hall effectelements, for example, a planar Hall element, a vertical Hall element,and a Circular Vertical Hall (CVH) element. As is also known, there aredifferent types of magnetoresistance elements, for example, asemiconductor magnetoresistance element such as Indium Antimonide(InSb), a giant magnetoresistance (GMR) element, for example, a spinvalve, an anisotropic magnetoresistance element (AMR), a tunnelingmagnetoresistance (TMR) element, and a magnetic tunnel junction (MTJ).The magnetic field sensing element may be a single element or,alternatively, may include two or more magnetic field sensing elementsarranged in various configurations, e.g., a half bridge or full(Wheatstone) bridge. Depending on the device type and other applicationrequirements, the magnetic field sensing element may be a device made ofa type IV semiconductor material such as Silicon (Si) or Germanium (Ge),or a type III-V semiconductor material like Gallium-Arsenide (GaAs) oran Indium compound, e.g., Indium-Antimonide (InSb).

Some of the above-described magnetic field sensing elements tend to havean axis of maximum sensitivity parallel (or in-plane) to a substratethat supports the magnetic field sensing element, and others of theabove-described magnetic field sensing elements tend to have an axis ofmaximum sensitivity perpendicular to a substrate that supports themagnetic field sensing element. In particular, planar Hall elements tendto have axes of sensitivity perpendicular to a substrate, while metalbased or metallic magnetoresistance elements (e.g., GMR, TMR, AMR) andvertical Hall elements tend to have axes of sensitivity parallel to asubstrate.

As used herein, the term “magnetic field sensor” is used to describe acircuit that uses a magnetic field sensing element, generally incombination with other circuits. Magnetic field sensors are used in avariety of applications, including, but not limited to, an angle sensorthat senses an angle of a direction of a magnetic field, a currentsensor that senses a magnetic field generated by a current carried by acurrent-carrying conductor, a magnetic switch that senses the proximityof a ferromagnetic object, a rotation detector that senses passingferromagnetic articles, for example, magnetic domains of a ring magnetor a ferromagnetic target (e.g., gear teeth) where the magnetic fieldsensor is used in combination with a back-biased or other magnet, and amagnetic field sensor that senses a magnetic field density of a magneticfield.

As used herein, the term “accuracy,” when referring to a magnetic fieldsensor, is used to refer to a variety of aspects of the magnetic fieldsensor. Illustrative sensors include current sensors, angle sensors,speed sensors and the like. These aspects include, but are not limitedto, an ability of the magnetic field sensor to: be a correctrepresentation of a static, alternating or varying sensed signals, havea minor dependence on the perturbations (background noise orinterferences), have minor dependence to its physical environment(temperature, stress), provide a repeatable output over cycling andaging, differentiate a gear tooth from a gear valley (or, moregenerally, the presence of a ferromagnetic object from the absence of aferromagnetic object) when the gear is not rotating and/or when the gearis rotating (or, more generally, when a ferromagnetic object is movingor not moving), an ability to differentiate an edge of a tooth of thegear from the tooth or the valley of the gear (or, more generally, theedge of a ferromagnetic object or a change in magnetization direction ofa hard ferromagnetic object), and a rotational accuracy with which theedge of the gear tooth is identified (or, more generally, the positionalaccuracy with which an edge of a ferromagnetic object or hardferromagnetic object can be identified). Ultimately, accuracy refers tooutput signal edge placement accuracy and consistency with respect togear tooth edges passing by the magnetic field sensor.

The terms “parallel” and “perpendicular” are used in various contextsherein. It should be understood that the terms parallel andperpendicular do not require exact perpendicularity or exactparallelism, but instead it is intended that normal manufacturingtolerances apply, which tolerances depend upon the context.

It is desirable for magnetic field sensors to achieve a certain level oramount of accuracy even in the presence of variations in an air gapbetween the magnetic field sensor and the gear that may change frominstallation to installation or from time to time. It is also desirablefor magnetic field sensors to achieve accuracy even in the presence ofvariations in relative positions of the magnet and the magnetic fieldsensing element within the magnetic field sensor. It is also desirablefor magnetic field sensors to achieve accuracy even in the presence ofunit-to-unit variations in the magnetic field generated by a magnetwithin the magnetic field sensors. It is also desirable for magneticfield sensors to achieve accuracy even in the presence of variations ofan axial rotation of the magnetic field sensors relative to the gear. Itis also desirable for magnetic field sensors to achieve accuracy even inthe presence of temperature variations of the magnetic field sensors.

Examples herein may describe a particular target, such as enginecamshaft ferromagnetic target. However, similar circuits and techniquescan be used with other cams or gears or ring magnets disposed upon theengine camshaft, or upon other rotating parts of an engine (e.g., crankshaft, transmission gear, anti-lock braking system (ABS), or uponrotating parts of a device that is not an engine. Other applications mayinclude linear translation sensors or other sensors where the target isnot a rotating gear. Magnetic sensors can be used with permanent magnets(ferrites, neodymium or any ferromagnetic materials), with currentflowing in coils (e.g. motor phases), with or without a magneticconcentrator or any sources of magnetic field (e.g. the earth).

The gear can have ferromagnetic gear teeth, which are generally softferromagnetic objects, but which can also be hard ferromagnetic objects,patterns, or domains which may or may not have actual physical changesin their shape. Also, while examples are shown below of magnetic fieldsensors that can sense ferromagnetic gear teeth or gear teeth edges upona gear configured to rotate, the magnetic field sensors can be used inother applications. The other applications include, but are not limitedto, sensing ferromagnetic objects upon a structure configured to movelinearly.

Example magnetic field sensors can have a variety of features that maybe described in one or more of the following U.S. Pat. Nos. or PatentPublications: 6,525,531, 6,278,269, 5,781,005, 7,777,607, 8,450,996,7,772,838, 7,253,614, 7,026,808, 8,624,588, 7,368,904, 6,693,419,8,729,892, 5,917,320, 6,091,239, 2012/0249126, all of which are hereinincorporated herein by reference.

FIG. 7 shows an exemplary computer 700 that can perform at least part ofthe processing described herein. The computer 700 includes a processor702, a volatile memory 704, a non-volatile memory 706 (e.g., hard disk),an output device 707 and a graphical user interface (GUI) 708 (e.g., amouse, a keyboard, a display, for example). The non-volatile memory 706stores computer instructions 712, an operating system 716 and data 718.In one example, the computer instructions 712 are executed by theprocessor 702 out of volatile memory 704. In one embodiment, an article720 comprises non-transitory computer-readable instructions.

Processing may be implemented in hardware, software, or a combination ofthe two. Processing may be implemented in computer programs executed onprogrammable computers/machines that each includes a processor, astorage medium or other article of manufacture that is readable by theprocessor (including volatile and non-volatile memory and/or storageelements), at least one input device, and one or more output devices.Program code may be applied to data entered using an input device toperform processing and to generate output information.

The system can perform processing, at least in part, via a computerprogram product, (e.g., in a machine-readable storage device), forexecution by, or to control the operation of, data processing apparatus(e.g., a programmable processor, a computer, or multiple computers).Each such program may be implemented in a high-level procedural orobject-oriented programming language to communicate with a computersystem. However, the programs may be implemented in assembly or machinelanguage. The language may be a compiled or an interpreted language andit may be deployed in any form, including as a stand-alone program or asa module, component, subroutine, or other unit suitable for use in acomputing environment. A computer program may be deployed to be executedon one computer or on multiple computers at one site or distributedacross multiple sites and interconnected by a communication network. Acomputer program may be stored on a storage medium or device (e.g.,CD-ROM, hard disk, or magnetic diskette) that is readable by a generalor special purpose programmable computer for configuring and operatingthe computer when the storage medium or device is read by the computer.Processing may also be implemented as a machine-readable storage medium,configured with a computer program, where upon execution, instructionsin the computer program cause the computer to operate.

Processing may be performed by one or more programmable processorsexecuting one or more computer programs to perform the functions of thesystem. All or part of the system may be implemented as, special purposelogic circuitry (e.g., an FPGA (field programmable gate array) and/or anASIC (application-specific integrated circuit)).

Having described exemplary embodiments of the invention, it will nowbecome apparent to one of ordinary skill in the art that otherembodiments incorporating their concepts may also be used. Theembodiments contained herein should not be limited to disclosedembodiments but rather should be limited only by the spirit and scope ofthe appended claims. All publications and references cited herein areexpressly incorporated herein by reference in their entirety.

What is claimed is:
 1. A method, comprising: receiving first signalsfrom a first signal source; receiving second signals from a secondsignal source, wherein the first and second signals are redundant; andcombining the first signals and the second signals to generate a firstoutput signal from the first signals, a second output signal from thesecond signals, and a third output signal from the first signals and thesecond signals.
 2. The method according to claim 1, further includinggenerating a fourth output signal from first and second signalsproviding uncertainty and/or risk information.
 3. The method accordingto claim 1, wherein the first signal source comprises a first transducerand the second signal source comprises a second transducer.
 4. Themethod according to claim 3, wherein the first and second transducersare substantially similar.
 5. The method according to claim 3, whereinthe first and second transducers are substantially dissimilar or ofdifferent nature.
 6. The method according to claim 1, wherein the firstsignal source comprises a first die and the second signal sourcecomprises a second die.
 7. The method according to claim 1, wherein thethird output signal comprises a combination, such as average, of thefirst and second signals.
 8. The method according to claim 7, whereinthe combination comprises an average.
 9. The method according to claim1, wherein the third output signal is more accurate than the first orsecond output signals taken independently.
 10. The method according toclaim 1, wherein the first and second signals each comprise sine andcosine values.
 11. The method according to claim 10, wherein the first,second, and third output signals each comprise processed signals fromtransducers.
 12. The method according to claim 1, further includinggenerating a fourth output signal from first and second signalsproviding risk information based on a comparison of similarity of thefirst signals and the second signals.
 13. The method according to claim12, wherein the comparison of similarity includes using a thresholdbased on degrees for angle signals generated from sine and cosinesignals.
 14. The method according to claim 1, further includingassigning a first error distribution to the first signals and a seconderror distribution to the second signals.
 15. The method according toclaim 14, further including assigning rectangular functions to the firstand second error distributions.
 16. The method according to claim 15,further including assigning a given number of standard deviations todefines the rectangular functions.
 17. The method according to claim 14,further including assigning Gaussian functions to the first and seconderror distributions.
 18. The method according to claim 14, furtherincluding determining an amount of overlap between the first and seconderror distributions.
 19. The method according to claim 18, furtherincluding determining a failure condition based on the amount ofoverlap.
 20. The method according to claim 19, further includingdetermining a level of confidence in the first and/or second signalsfrom the amount of overlap or intersection of distributions.
 21. Themethod according to claim 18, further including determining a bestestimate for the first and/or second signals from the amount of overlap.22. A system, comprising: a first signal source configured to generatefirst signals; a second signal source to generate second signals,wherein the first and second signals are redundant; and a signalprocessing module configure to combine the first signals and the secondsignals to generate a first output signal from the first signals, asecond output signal from the second signals, and a third output signalfrom the first signals and the second signals.
 23. The system accordingto claim 22, wherein the signal processing module is further configuredto generate a fourth output signal from first and second signalsproviding risk information.
 24. The system according to claim 22,wherein the first signal source comprises a first transducer and thesecond signal source comprises a second transducer.
 25. The systemaccording to claim 24, wherein the first and second transducers aresubstantially similar.
 26. The system according to claim 22, wherein thefirst signal source comprises a first die and the second signal sourcecomprises a second die.
 27. The system according to claim 22, whereinthe third output signal comprises a combination, of the first and secondsignals.
 28. The system according to claim 22, wherein the third outputsignal is more accurate than the first or second output signals.
 29. Thesystem according to claim 22, wherein the first and second signals eachcomprise sine and cosine values.
 30. The system according to claim 29,wherein the first, second, and third output signals each comprise anangle output signal.
 31. The system according to claim 22, furtherincluding generating a fourth output signal from first and secondsignals providing risk information based on a comparison of similarityof the first signals and the second signals.
 32. The system according toclaim 31, wherein the comparison of similarity includes using athreshold based on degrees for angle signals generated from sine andcosine signals.
 33. The system according to claim 22, further includingassigning a first error distribution to the first signals and a seconderror distribution to the second signals.
 34. The system according toclaim 33, further including assigning rectangular functions to the firstand second error distributions.
 35. The system according to claim 34,further including assigning a given number of standard deviations todefines the rectangular functions.
 36. The system according to claim 34,further including determining an amount of overlap between the first andsecond error distributions.
 37. The system according to claim 36,further including determining a failure condition based on the amount ofoverlap.
 38. The system according to claim 36, further includingdetermining a level of confidence in the first and/or second signalsfrom the amount of overlap.
 39. The system according to claim 36,further including determining a best estimate for the first and/orsecond signals from the amount of overlap.
 40. The system according toclaim 33, further including assigning Gaussian functions to the firstand/or second error distributions.
 41. A system, comprising: a firstsignal source means for generating first signals; a second signal sourcemeans for generating second signals, wherein the first and secondsignals are redundant; and a signal processing means for combining thefirst signals and the second signals to generate a first output signalfrom the first signals, a second output signal from the second signals,and a third output signal from the first signals and the second signals.42. The system according to claim 41, wherein the signal processingmeans further generates a fourth output signal from first and secondsignals providing risk information.
 43. The system according to claim41, wherein the first signal source means comprises a first transducerand the second signal source means comprises a second transducer. 44.The system according to claim 43, wherein the first and secondtransducers are substantially similar.
 45. The system according to claim41, wherein the first signal source means comprises a first die and thesecond signal source means comprises a second die.